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Such an expansion is also isothermal and may have the same initial and final states as in the reversible expansion. Since entropy is a state function (that depends on an equilibrium state, not depending on a path that the system takes to reach that state), the change in entropy of the system is the same as in the reversible process and is given ...
The entropy of a given mass does not change during a process that is internally reversible and adiabatic. A process during which the entropy remains constant is called an isentropic process, written Δ s = 0 {\displaystyle \Delta s=0} or s 1 = s 2 {\displaystyle s_{1}=s_{2}} . [ 12 ]
[16] [17] Through the efforts of Clausius and Kelvin, the work done by a reversible heat engine was found to be the product of the Carnot efficiency (i.e., the efficiency of all reversible heat engines with the same pair of thermal reservoirs) and the heat absorbed by a working body of the engine during isothermal expansion: = = To derive the ...
The dependence of work on the path of the thermodynamic process is also unrelated to reversibility, since expansion work, which can be visualized on a pressure–volume diagram as the area beneath the equilibrium curve, is different for different reversible expansion processes (e.g. adiabatic, then isothermal; vs. isothermal, then adiabatic ...
The Otto Cycle is an example of a reversible thermodynamic cycle. 1→2: Isentropic / adiabatic expansion: Constant entropy (s), Decrease in pressure (P), Increase in volume (v), Decrease in temperature (T) 2→3: Isochoric cooling: Constant volume(v), Decrease in pressure (P), Decrease in entropy (S), Decrease in temperature (T)
Mathematically, the absolute entropy of any system at zero temperature is the natural log of the number of ground states times the Boltzmann constant k B = 1.38 × 10 −23 J K −1. The entropy of a perfect crystal lattice as defined by Nernst's theorem is zero provided that its ground state is unique, because ln(1) = 0.
The temperature-entropy conjugate pair is concerned with the transfer of energy, especially for a closed system. An isothermal process occurs at a constant temperature. An example would be a closed system immersed in and thermally connected with a large constant-temperature bath. Energy gained by the system, through work done on it, is lost to ...
An example of a quasi-static process that is not idealizable as reversible is slow heat transfer between two bodies on two finitely different temperatures, where the heat transfer rate is controlled by a poorly conductive partition between the two bodies. In this case, no matter how slowly the process takes place, the state of the composite ...